Question

Let x and y be two real numbers, then which of the following is always true ?

• A. $|\text{x} - \text{y}| \le |\text{x}| - |\text{y}|$
• B. $|\text{x} - \text{y}| \le |\text{x}| + |\text{y}|$
• C. $|\text{x} + \text{y}| \le |\text{x}| - |\text{y}|$
• D. $|\text{x} + \text{y}| \ge |\text{x}| + |\text{y}|$

Hint:

The absolute value of the sum or difference of two numbers is always less than or equal to the sum of their individual absolute values:
\[ |x \pm y| \le |x| + |y| \]
This is the most common form of the Triangle Inequality.

Answer 1

The Correct Option is B